Question

Let $f\left(x\right)$ be an even function & even degree polynomial such that $f\left(\begin{array}{c}\frac{1}{2}\end{array}\right)=\frac{1}{2},f\left(1\right)=1,f\left(2\right)=-3,f\left(3\right)=5$ then minimum number of points of intersection for $f\left(x\right)$ is

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$4$

$f^{\prime }(-x_1)=f^{\prime }(-x_2)=f^{\prime }\left(0\right)=f^{\prime }\left(x_2\right)=f^{\prime }\left(x_1\right)=0$
By using Rolle's theorem, minimum number of points of inflection are four.